The k-Dominating Graph
نویسندگان
چکیده
Given a graphG, the k-dominating graph ofG, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. The graph Dk(G) aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions and deletions, such that the intermediate set of vertices at each step is a dominating set if and only if they are in the same connected component of Dk(G). In this paper we give conditions that ensure Dk(G) is connected.
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 30 شماره
صفحات -
تاریخ انتشار 2014